| 一类高阶周期系数线性微分方程解的性质 |
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| 引用本文： | 陈宗煊. 一类高阶周期系数线性微分方程解的性质[J]. 数学学报, 2006, 49(5): 989-998. DOI: cnki:ISSN:0583-1431.0.2006-05-004 |
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| 作者姓名： | 陈宗煊 |
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| 作者单位： | 华南师范大学数学系,广州510631 |
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| 基金项目： | 国家自然科学基金资助项目（10161006）;广东省自然科学基金资助项目（04010360）致谢作者感谢审稿人对本文提出了宝贵的修改意见. |
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| 摘 要： | 本文主要研究了一类高阶周期系数线性微分方程解的超级,e-型级,相关性等问题,并得到了e-型级与超级之间的一些关系,以及这两种级与系数的精确关系．本文是首次使用e-型级来估计方程解的增长性,这种估计比级,超级更为精确．
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| 关 键 词： | 线性微分方程 周期函数 线性无关 |
| 文章编号： | 0583-1431（2006）05-0989-10 |
| 收稿时间： | 2004-11-15 |
| 修稿时间： | 2004-11-152005-05-30 |
The Property of Solutions for a Class of Higher Order Linear DiflFerential Equations with Periodic Coefficients |
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| Zong Xuan CHEN. The Property of Solutions for a Class of Higher Order Linear DiflFerential Equations with Periodic Coefficients[J]. Acta Mathematica Sinica, 2006, 49(5): 989-998. DOI: cnki:ISSN:0583-1431.0.2006-05-004 |
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| Authors: | Zong Xuan CHEN |
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| Affiliation: | Department of Mathematics, South China Normal University, Guangzhou 510631, P. R. China |
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| Abstract: | In this paper we investigate the problems on the hyper-order, the e-type order, the dependence relation of solutions for a class of higher order linear differential equations with periodic coefficients, and obtain some relations between e-type order and hyper-order, and precise relations between the two orders and coefficients. In this paper, using e-type order to estimate the growth of solutions of the equations is the first, the estimation is more precise than that using the order or the hyper-order. |
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| Keywords: | Linear differential equation Periodic function Linearly independent |
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